Package 'HBV.IANIGLA'

Alerce's glacier data for modeling

Description

A dataset containing all necessary information to simulate a three year glacier surface mass balance. The ice body is located on Monte Tronador, nearby the border between Argentina and Chile in the Andes of Northern Patagonia. Alerce is a medium size mountain glacier with an area of about 2.33 km2 that ranges between 1629 and 2358 masl and it shows a SE aspect (IANIGLA-ING, 2018).

Usage

alerce_data

Format

A list with five elements

mass_balance

data frame with the estimated annual mass balance and the acceptable uncertainty bounds.

mb_dates

data frame containing the first fix days of the winter and summer mass balances.

meteo_data

data frame with the precipitation gauge and air temperatures records. The former series is recorded at Puerto Montt's station (Chile) and the last one is measured at Bariloche's airport (Argentina)

topography

data frame with: elevation zone number, minimum, maximum and mean altitude values for the elevation range and the relative area.

station_height

numeric vector with the stations heights. Air temperature refers to Bariloche's airport and precipitation to Puerto Montt station. Units are in masl (meters above sea level).

References

IANIGLA-ING. IANIGLA-Inventario Nacional de Glaciares. 2018. Informe de las subcuencas de los ríos Manso, Villegas y Foyel. Cuenca de los ríos Manso y Puelo. IANIGLA-CONICET, Ministerio de Ambiente y Desarrollo Sustentable de la Nación. Technical report, IANIGLA, 2018b.[p8]

---

Hargreaves reference evapotranspiration

Description

Computes crop reference evapotranspiration using Hargreaves equation (Hargreaves and Allen, 2003).

Usage

do_evap_hargreaves(
       m_tmean,
       m_tmax,
       m_tmin,
       m_kin
       )

Arguments

m_tmean	numeric matrix with daily mean air temperature $[°C]$ (ncol = number of zones).
m_tmax	numeric matrix with daily maximum air temperature $[°C]$ (ncol = number of zones).
m_tmin	numeric matrix with daily minimum air temperature $[°C]$ (ncol = number of zones).
m_kin	numeric matrix with daily total incoming extraterrestrial solar radiation $[MJ/(m^2 day)]$ (ncol = number of zones).

Value

List object with the following numeric matrices (ncol = number of zones):

1. evap_ref $[mm/day]$.

Note

The equation used by the model is:

$ET_o = 0.0023 * (T_{mean} + 17.8) * (T_{max} - T_{min})^{0.5} * Ra * 0.408$

if the temperature value is below $0°C$, the model sets it to $0°C$. The $0.408$ value is to convert $[MJ/(m^2 day)]$ to $[mm/day]$.

---

Glacier melt routine

Description

Allows you to simulate snow accumulation, snow and ice melting processes using a temperature index approach.

Usage

do_glacier(
       m_tair,
       m_rainfall,
       m_snowfall,
       v_glacier_vol,
       swe_init,
       m_param
       )

Arguments

m_tair	numeric matrix with air temperatures $[°C/\Delta t]$ (ncol = number of zones).
m_rainfall	numeric matrix with rainfall $[mm/\Delta t]$ (ncol = number of zones).
m_snowfall	numeric matrix with snowfall $[mm/\Delta t]$ (ncol = number of zones).
v_glacier_vol	numeric vector with glacier volume $[mm \, we]$ (length = number of zones).
swe_init	double with initial snow water equivalent over the glacier $[mm]$.
m_param	numeric matrix with parameters (ncol = number of zones): SFCF: snowfall correction factor $[-]$. Tt: melt temperature $[ºC]$. fm: snowmelt factor $[mm/°C.\Delta t]$. fi: icemelt factor $[mm/°C.\Delta t]$. dt: air temperature decrements $[ºC]$. This value will be subtracted from the air temperature series to take into account over-glacier reduced temperatures (regarding it's surroundings).

Value

List object with the following numeric matrices (ncol = number of zones):

1. rainfall $[mm/\Delta t]$.

2. snowfall $[mm/\Delta t]$.

3. swe $[mm/\Delta t]$.

4. snow_melt $[mm/\Delta t]$.

5. ice_melt $[mm/\Delta t]$.

6. total_melt = snow_melt + ice_melt $[mm/\Delta t]$.

7. ice_vol $[mm]$.

8. cum = snowfall - total_melt $[mm/\Delta t]$.

9. water = rainfall + total_melt $[mm/\Delta t]$.

---

Glacier routing bucket function

Description

Implement a conceptual water storage and release formulation for glacier runoff routing (Glacier_Disch).

Usage

do_glacier_route(
       model,
       m_input,
       init_cond,
       v_param
       )

Arguments

model	numeric integer with the model's choice. The current HBV.IANIGLA version only supports the S08 approach (see Glacier_Disch).
m_input	numeric matrix with two columns: Model 1 column_1: snow water equivalent above the glacier $[mm/\Delta t]$. The series can be obtained from the do_glacier function previously rescaled (do_rescale). column_2: melted snow + melted ice + rainfall $[mm/\Delta t]$. The series can be obtained from the do_glacier function previously rescaled (do_rescale).
init_cond	numeric value with the initial glacier reservoir water content SG $[mm]$.
v_param	numeric vector with the following values: Model 1 (S08) KGmin: minimal outflow rate $[1/\Delta t]$. dKG: maximum outflow rate increase $[1/\Delta t]$. AG: scale factor $[mm]$.

Value

Numeric matrix with the following columns:

Model 1 (S08)

• Q: glacier discharge $[mm/\Delta t]$.

• SG: glacier's bucket water storage content series $[1/\Delta t]$.

---

Run HBV model

Description

do_hbv allows you to run a full hydro-glaciological model at once. This function is designed to facilitate the use of the package, internally coupling all the modules that HBV.IANIGLA offers. The user only has to take care of providing the input data, initial conditions and parameters.

Usage

do_hbv(data_hipso,
       data_meteo,
       data_shortwave,
       station_altitude,
       rh_option = "e_vap",
       pphase_model = "harder",
       pphase_period = "1 day",
       tair_param,
       precip_param,
       snow_init,
       snow_param,
       glacier_init,
       glacier_param,
       glacier_route_init,
       glacier_route_param,
       soil_init,
       soil_param,
       route_model,
       route_init,
       route_param,
       transfer_param)

Arguments

data_hipso	data frame, data frame extension (e.g. a tibble), or a lazy data frame (e.g. from dbplyr or dtplyr) with the following columns (respect the column names): elev_band: numeric column with the number of the elevation zone. hmin: numeric column with the lower elevation of the elevation band $[masl]$. hmean: numeric column with the mean elevation of the elevation band $[masl]$. hmax: numeric column with the highest elevation of the elevation band $[masl]$. total_area: numeric column with the total area of the elevation band $[km^2]$. glacier_area: numeric column with the area covered by ice in the elevation band $[km^2]$.
data_meteo	data frame, data frame extension (e.g. a tibble), or a lazy data frame (e.g. from dbplyr or dtplyr) with the following columns (respect the column names): date: date column with the dates of register meteorological data. tmin: numeric vector with daily minimum air temperature $[°C]$. tmean: numeric vector with daily mean air temperature $[°C]$. tmax: numeric vector with daily maximum air temperature $[°C]$. rh: numeric vector with daily mean relative humidity $[\%]$. precip: numeric vector with daily total precipitation $[mm]$.
data_shortwave	data frame, data frame extension (e.g. a tibble), or a lazy data frame (e.g. from dbplyr or dtplyr) with the following columns (respect the column names): date: date column with the dates. They should be the same of data_meteo kin_i: daily total incoming extraterrestrial solar radiation $[MJ/(m^2 day)]$. The number of columns should be the same as number of elevation bands (ncol = number of zones).
station_altitude	numeric vector with two elements: air temperature and relative humidity station altitude $[masl]$. precipitation station altitude $[masl]$. The values are used to extrapolate these variables to other altitudes in the basin.
rh_option	string with assumption used to extrapolate relative humidity to other altitudes: "e_vap": assumes that vapour pressure is constant over all altitudes. This value will be constrain to rh = 100 %. "rh": assumes constant relative humidity over all altitudes.
pphase_model	string with model's choice: "harder" - "ding". Default is set to "harder". See the works of Harder and Pomeroy (2013) or Ding et al. (2014) for more details.
pphase_period	string with one of the following options (just for pphase_model = "harder"): * "15 min" * "1 hour" * "1 day"
tair_param	numeric vector with the following parameters: air temperature linear gradient [ºC/km]. E.g.: $-6.5$. threshold height. Air temperature does not decrease when the altitude is higher than this value $[masl]$.
precip_param	numeric vector with the following parameters: precipitation linear gradient increment [%/100 m]. threshold height. Precipitation does not decrease when the altitude is higher than this value $[masl]$.
snow_init	double with initial snow water equivalent $[mm]$. See also SnowGlacier_HBV.
snow_param	numeric matrix with the following parameters (ncol = number of zones - see also SnowGlacier_HBV): SFCF: snowfall correction factor $[-]$. Tt: melt temperature $[ºC]$. fm: snowmelt factor $[mm/°C.\Delta t]$.
glacier_init	numeric vector with the following initial values (see also SnowGlacier_HBV), double with initial snow water equivalent over glaciers $[mm we]$. double with initial glacier volume over the entire basin $[mm we]$.
glacier_param	numeric matrix with the following parameters (ncol = number of zones): fi: icemelt factor $[mm/°C.\Delta t]$. dt: air temperature decrements $[ºC]$. This value will be subtracted from the air temperature series to take into account over-glacier reduced temperatures (regarding it's surroundings). SFCF, Tt and fm are recycled from snow_param. See also SnowGlacier_HBV.
glacier_route_init	numeric value with the initial glacier reservoir water content SG $[mm]$. See also Glacier_Disch.
glacier_route_param	numeric vector with the following parameters (see Glacier_Disch): KGmin: minimal outflow rate $[1/\Delta t]$. dKG: maximum outflow rate increase $[1/\Delta t]$. AG: scale factor $[mm]$.
soil_init	double with initial soil water content $[mm]$.
soil_param	numeric matrix with the following parameters (ncol = number of zones - see Soil_HBV for more details): FC: fictitious soil field capacity $[mm]$. LP: parameter to get actual ET $[-]$. $\beta$: exponential value that allows for non-linear relations between soil box water input (qflow = melt + rainfall) and the effective runoff $[-]$.
route_model	numeric integer indicating which reservoir formulation to use (see Routing_HBV).
route_init	numeric vector with initial state variables (see Routing_HBV's initCond argument).
route_param	numeric vector with model parameters (see Routing_HBV's param argument).
transfer_param	numeric vector with the base transfer function (see UH).

Value

A list with the following elements:

References

1. Harder, P., Pomeroy, J.W., Westbrook, C.J., 2015. Hydrological resilience of a Canadian Rockies headwaters basin subject to changing climate, extreme weather, and forest management. Hydrological Processes 29, 3905–3924. https://doi.org/10.1002/hyp.10596

2. Ding, B., Yang, K., Qin, J., Wang, L., Chen, Y., He, X., 2014. The dependence of precipitation types on surface elevation and meteorological conditions and its parameterization. Journal of Hydrology 513, 154–163. https://doi.org/10.1016/j.jhydrol.2014.03.038

---

Run HBV model

Description

do_hbv_run allows you to run a full hydro-glaciological model at once. This function is designed to facilitate the use of the package, internally coupling all the modules that HBV.IANIGLA offers. The user only has to take care of providing the input data, initial conditions and parameters.

Usage

do_hbv_run(
       data_hipso,
       data_meteo,
       data_shortwave,
       station_altitude,
       rh_option,
       pphase_model,
       pphase_period,
       tair_param,
       precip_param,
       snow_init,
       snow_param,
       glacier_init,
       glacier_param,
       glacier_route_init,
       glacier_route_param,
       soil_init,
       soil_param,
       route_model,
       route_init,
       route_param,
       transfer_param)

Arguments

data_hipso	data frame, data frame extension (e.g. a tibble), or a lazy data frame (e.g. from dbplyr or dtplyr) with the following columns (respect the column names): elev_band: numeric column with the number of the elevation zone. hmin: numeric column with the lower elevation of the elevation band $[masl]$. hmean: numeric column with the mean elevation of the elevation band $[masl]$. hmax: numeric column with the highest elevation of the elevation band $[masl]$. total_area: numeric column with the total area of the elevation band $[km^2]$. glacier_area: numeric column with the area covered by ice in the elevation band $[km^2]$.
data_meteo	data frame, data frame extension (e.g. a tibble), or a lazy data frame (e.g. from dbplyr or dtplyr) with the following columns (respect the column names): date: date column with the dates of register meteorological data. tmin: numeric vector with daily minimum air temperature $[°C]$. tmean: numeric vector with daily mean air temperature $[°C]$. tmax: numeric vector with daily maximum air temperature $[°C]$. rh: numeric vector with daily mean relative humidity $[\%]$. precip: numeric vector with daily total precipitation $[mm]$.
data_shortwave	data frame, data frame extension (e.g. a tibble), or a lazy data frame (e.g. from dbplyr or dtplyr) with the following columns (respect the column names): date: date column with the dates. They should be the same of data_meteo kin_i: daily total incoming extraterrestrial solar radiation $[MJ/(m^2 day)]$. The number of columns should be the same as number of elevation bands (ncol = number of zones).
station_altitude	numeric vector with two elements: air temperature and relative humidity station altitude $[masl]$. precipitation station altitude $[masl]$. The values are used to extrapolate these variables to other altitudes in the basin.
rh_option	string with assumption used to extrapolate relative humidity to other altitudes: "e_vap": assumes that vapour pressure is constant over all altitudes. This value will be constrain to rh = 100 %. "rh": assumes constant relative humidity over all altitudes.
pphase_model	string with model's choice: "harder" - "ding". Default is set to "harder". See the works of Harder and Pomeroy (2013) or Ding et al. (2014) for more details.
pphase_period	string with one of the following options (just for pphase_model = "harder"): "15 min" "1 hour" "1 day"
tair_param	numeric vector with the following parameters: air temperature linear gradient [ºC/km]. E.g.: $-6.5$. threshold height. Air temperature does not decrease when the altitude is higher than this value $[masl]$.
precip_param	numeric vector with the following parameters: precipitation linear gradient increment [%/100 m]. threshold height. Precipitation does not decrease when the altitude is higher than this value $[masl]$.
snow_init	double with initial snow water equivalent $[mm]$. See also SnowGlacier_HBV.
snow_param	numeric matrix with the following parameters (ncol = number of zones - see also SnowGlacier_HBV): SFCF: snowfall correction factor $[-]$. Tt: melt temperature $[ºC]$. fm: snowmelt factor $[mm/°C.\Delta t]$.
glacier_init	numeric vector with the following initial values (see also SnowGlacier_HBV), double with initial snow water equivalent over glaciers $[mm we]$. double with initial glacier volume over the entire basin $[mm we]$.
glacier_param	numeric matrix with the following parameters (ncol = number of zones): fi: icemelt factor $[mm/°C.\Delta t]$. dt: air temperature decrements $[ºC]$. This value will be subtracted from the air temperature series to take into account over-glacier reduced temperatures (regarding it's surroundings). SFCF, Tt and fm are recycled from snow_param. See also SnowGlacier_HBV.
glacier_route_init	numeric value with the initial glacier reservoir water content SG $[mm]$. See also Glacier_Disch.
glacier_route_param	numeric vector with the following parameters (see Glacier_Disch): KGmin: minimal outflow rate $[1/\Delta t]$. dKG: maximum outflow rate increase $[1/\Delta t]$. AG: scale factor $[mm]$.
soil_init	double with initial soil water content $[mm]$.
soil_param	numeric matrix with the following parameters (ncol = number of zones - see Soil_HBV for more details): FC: fictitious soil field capacity $[mm]$. LP: parameter to get actual ET $[-]$. $\beta$: exponential value that allows for non-linear relations between soil box water input (qflow = melt + rainfall) and the effective runoff $[-]$.
route_model	numeric integer indicating which reservoir formulation to use (see Routing_HBV).
route_init	numeric vector with initial state variables (see Routing_HBV's initCond argument).
route_param	numeric vector with model parameters (see Routing_HBV's param argument).
transfer_param	numeric vector with the base transfer function (see UH).

Value

A list with the following elements:

References

1. Harder, P., Pomeroy, J.W., Westbrook, C.J., 2015. Hydrological resilience of a Canadian Rockies headwaters basin subject to changing climate, extreme weather, and forest management. Hydrological Processes 29, 3905–3924. https://doi.org/10.1002/hyp.10596

2. Ding, B., Yang, K., Qin, J., Wang, L., Chen, Y., He, X., 2014. The dependence of precipitation types on surface elevation and meteorological conditions and its parameterization. Journal of Hydrology 513, 154–163. https://doi.org/10.1016/j.jhydrol.2014.03.038

---

Precipitation phase partitioning

Description

Allows you to estimate precipitation phase using a the model proposed by Ding et al. (2014).

Usage

do_pphase_ding(
       m_tair,
       m_rh,
       m_precip,
       v_altitude
       )

Arguments

m_tair	numeric matrix with air temperatures $[°C/\Delta t]$ (ncol = number of zones).
m_rh	numeric matrix with relative humidity $[\%]$ (ncol = number of zones).
m_precip	numeric matrix with total precipitation $[mm/\Delta t]$ (ncol = number of zones).
v_altitude	numeric vector with the mean altitude of each elevation zone $[masl]$ (length = number of zones).

Value

List object with the following numeric matrices (ncol = number of zones):

1. rainfall $[mm/\Delta t]$.

2. snowfall $[mm/\Delta t]$.

Note

The model was developed using daily data.

---

Precipitation phase partitioning

Description

Allows you to estimate precipitation phase using a psychrometric energy balance method (Harder and Pomeroy, 2013).

Usage

do_pphase_harder(
       m_tair,
       m_rh,
       m_precip,
       period = "1 day"
       )

Arguments

m_tair	numeric matrix with air temperatures $[°C/\Delta t]$ (ncol = number of zones).
m_rh	numeric matrix with relative humidity $[\%]$ (ncol = number of zones).
m_precip	numeric matrix with total precipitation $[mm/\Delta t]$ (ncol = number of zones).
period	string with the recorded precipitation time-step: "1 day" (default). "1 hour". "15 min".

Value

List object with the following numeric matrices (ncol = number of zones):

1. rainfall $[mm/\Delta t]$.

2. snowfall $[mm/\Delta t]$.

---

Precipitation extrapolation model

Description

Computes precipitation using an extrapolation linear model.

Usage

do_precip_gradient(
       v_precip,
       station_alt,
       v_altitude,
       v_grad
       )

Arguments

v_precip	numeric vector with precipitation series $[mm]$.
station_alt	altitude of the precipitation station $[masl]$
v_altitude	numeric vector with target altitudes $[masl]$ (length = number of zones).
v_grad	numeric vector with the following elements: precipitation linear gradient increment [%/100 m]. threshold height. Precipitation does not decrease when the altitude is higher than this value $[masl]$.

Value

List with extrapolated precipitation numeric matrix (ncol = number of zones).

---

Rescale function

Description

Allows you to rescale the zone outputs (from do_xx routines) into a single response using relative areas.

Usage

do_rescale(
       x,
       area
       )

Arguments

x	list output coming from do_xx routines.
area	numeric vector with relative area of every zone (length = number of zones = matrix columns).

Value

Numeric matrix with do_xx routine variables scaled according to area argument.

---

Relative humidity extrapolation model

Description

Computes relative humidity using an extrapolation linear model.

Usage

do_rh_gradient(
       v_tair,
       v_rh,
       station_alt,
       v_altitude,
       v_grad,
       option = "e_vap"
       )

Arguments

v_tair	numeric vector with air temperatures series $[°C]$.
v_rh	numeric vector with relative humidity series $[\%]$.
station_alt	altitude of the air temperature and relative humidity stations $[masl]$.
v_altitude	numeric vector with target altitudes $[masl]$ (length = number of zones).
v_grad	numeric vector with the following elements: air temperature linear gradient [ºC/km]. E.g.: $-6.5$. threshold height. Air temperature does not decrease when the altitude is higher than this value $[masl]$.
option	string with: "e_vap": assumes that vapour pressure is constant over all altitudes (v_altitude). This value will be constrain to rh = 100 %. "rh": assumes constant relative humidity over all altitudes (v_altitude).

Value

List with extrapolated relative humidity numeric matrix with (ncol = number of zones).

---

Routing bucket function

Description

Implement one of the five different bucket formulations for runoff routing. The output of this function is the input series of the transfer function (do_transfer).

Usage

do_route(
       model,
       v_recharge,
       v_init_cond,
       v_param
       )

Arguments

model	numeric integer indicating which reservoir formulation to use (see Routing_HBV).
v_recharge	numeric vector with recharge from soil routine (after applying do_rescale).
v_init_cond	numeric vector with initial state variables (see Routing_HBV's initCond argument).
v_param	numeric vector with model parameters (see Routing_HBV's param argument).

Value

Numeric matrix with the columns depending upon model choice (see Routing_HBV).

---

Snow accumulation and melt routine

Description

Allows you to simulate snow accumulation and melting processes using a temperature index approach.

Usage

do_snow(
       m_tair,
       m_rainfall,
       m_snowfall,
       swe_init,
       m_param
       )

Arguments

m_tair	numeric matrix with air temperatures $[°C/\Delta t]$ (ncol = number of zones).
m_rainfall	numeric matrix with rainfall $[mm/\Delta t]$ (ncol = number of zones).
m_snowfall	numeric matrix with snowfall $[mm/\Delta t]$ (ncol = number of zones).
swe_init	double with initial snow water equivalent $[mm]$.
m_param	numeric matrix with parameters (ncol = number of zones): SFCF: snowfall correction factor $[-]$. Tt: melt temperature $[ºC]$. fm: snowmelt factor $[mm/°C.\Delta t]$.

Value

List object with the following numeric matrices (ncol = number of zones):

1. rainfall $[mm/\Delta t]$.

2. snowfall $[mm/\Delta t]$.

3. swe $[mm/\Delta t]$.

4. melt $[mm/\Delta t]$.

5. qflow: rainfall + melt $[mm/\Delta t]$.

---

Soil moisture routine

Description

Allows you to account for actual evapotranspiration, abstractions, antecedent conditions and effective runoff. The formulation enables non linear relationships between soil box water input (rainfall plus snowmelt) and the effective runoff.

Usage

do_soil(
       m_qflow,
       m_pet,
       m_swe,
       swc,
       m_param
       )

Arguments

m_qflow	numeric matrix with total water generated in do_snow $[mm/\Delta t]$ (ncol = number of zones).
m_pet	numeric matrix with potential evapotranspiration $[mm/\Delta t]$ (ncol = number of zones).
m_swe	numeric matrix with snow water equivalent simulations (from do_snow) $[mm/\Delta t]$ (ncol = number of zones).
swc	double with initial soil water content $[mm]$.
m_param	numeric matrix with parameters (ncol = number of zones): FC: fictitious soil field capacity $[mm]$. LP: parameter to get actual ET $[-]$. $\beta$: exponential value that allows for non-linear relations between soil box water input (qflow = melt + rainfall) and the effective runoff $[-]$.

Value

List object with the following numeric matrices (ncol = number of zones):

1. soil_moisture $[mm/\Delta t]$.

2. actual_evap $[mm/\Delta t]$.

3. recharge $[mm/\Delta t]$.

---

Air temperature extrapolation model

Description

Computes air temperature using an extrapolation linear model.

Usage

do_tair_gradient(
       v_tair,
       station_alt,
       v_altitude,
       v_grad
       )

Arguments

v_tair	numeric vector with air temperatures series $[°C]$.
station_alt	altitude of the air temperature station $[masl]$
v_altitude	numeric vector with target altitudes $[masl]$ (length = number of zones).
v_grad	numeric vector with the following elements: air temperature linear gradient [ºC/km]. E.g.: $-6.5$. threshold height. Air temperature does not decrease when the altitude is higher than this value $[masl]$.

Value

List with extrapolated air temperatures numeric matrix (ncol = number of zones).

---

Transfer function

Description

Use a triangular transfer function to adjust the timing of the simulated streamflow discharge. This module represents the runoff routing in the streams.

Usage

do_transfer(
       model,
       v_qflow,
       v_param
       )

Arguments

model	numeric integer with the transfer function model (see UH).
v_qflow	numeric vector with the water that gets into the stream (see UH).
v_param	numeric vector with the base transfer function (see UH).

Value

Numeric vector with the simulated streamflow discharge.

---

Markov Chain

Description

Creates a set of K chains.

Arguments

v_param_lwr	numeric vector with lower bound parameters.
v_param_upp	numeric vector with upper bound parameters.
K	number of chains to create.

Value

List with K initial matrices.

---

Update parameters

Description

Decides which parameter to update

Arguments

n_param	integer with parameter vector size.
CR	integer with crossover values. It defines the size of the probability vector.

Value

Integer binary vector. A 1 value indicates parameter update.

---

rowbind

Description

Binds a numeric vector v as the new last row of the numeric matrix m.

Arguments

m	numeric matrix
v	numeric vector

Value

Numeric matrix

---

Saturated water vapor pressure

Description

Calculates e*

Arguments

tair	a double with air temperature $[ºC]$.

Value

A double with saturated water vapor pressure $[kPa]$.

---

Glacier discharge conceptual model

Description

Implement the conceptual water storage and release formulation for glacier runoff routing. The current model version follows the approach proposed by Stahl et al. (2008) (hereafter S08) for the Bridge River basin. Note that the bucket storage and release concepts for glacier runoff modeling are also described in Jansson et al. (2002).

Usage

Glacier_Disch(
       model,
       inputData,
       initCond,
       param
       )

Arguments

model	numeric integer with the model's choice. The current HBV.IANIGLA version only supports the S08 approach. 1:S08 glacier storage and release model.
inputData	numeric matrix with two columns: Model 1 column_1: snow water equivalent above the glacier $[mm/\Delta t]$. The series can be obtained from the SnowGlacier_HBV function output. column_2: melted snow + melted ice + rainfall $[mm/\Delta t]$. This series comes from the TotScal column in the SnowGlacier_HBV function output.
initCond	numeric value with the initial glacier reservoir water content SG $[mm]$.
param	numeric vector with the following values: Model 1 (S08) KGmin: minimal outflow rate $[1/\Delta t]$. dKG: maximum outflow rate increase $[1/\Delta t]$. AG: scale factor $[mm]$.

Value

Numeric matrix with the following columns:

Model 1 (S08)

• Q: glacier discharge $[mm/\Delta t]$.

• SG: glacier's bucket water storage content series $[1/\Delta t]$.

References

Jansson, P., Hock, R., Schneider, T., 2003. The concept of glacier storage: a review. J. Hydrol., Mountain Hydrology and Water Resources 282, 116–129. https://doi.org/10.1016/S0022-1694(03)00258-0

Stahl, K., Moore, R.D., Shea, J.M., Hutchinson, D., Cannon, A.J., 2008. Coupled modelling of glacier and streamflow response to future climate scenarios. Water Resour. Res. 44, W02422. https://doi.org/10.1029/2007WR005956

Examples

# The following is a toy example. I strongly recommend to see
# the package vignettes in order to improve your skills on HBV.IANIGLA

## Create an input data and run the module
DataMatrix <- cbind(
                    runif(n = 100, min = 0, max = 50),
                    runif(n = 100, min = 0, max = 200)
                    )

dischGl    <- Glacier_Disch(model = 1, inputData = DataMatrix,
                           initCond = 100, param = c(0.1, 0.9, 10))

---

Synthetic glacio-hydrological data for modeling

Description

A dataset containing all the necessary information to simulate almost 15 year of catchment streamflow in a synthetic basin. This example was though to improve user's skills on the HBV.IANIGLA.

Usage

glacio_hydro_hbv

Format

A list with five elements

basin

data frame containing elevation band names and the hypsometric values for modeling the catchment.

tair

numeric matrix with the air temperature series (columns) for the 15 elevation bands.

prec

numeric matrix with the precipitation series (columns) for the 15 elevation bands.

pet

numeric matrix with the potential evapotranspiration series (columns) for the 15 elevation bands.

qout

numeric matrix containing the total basin discharge, the streamflow coming from the soil portion of the basin and the part that is generated in the glaciers.

---

Lumped HBV catchment data

Description

Here you will find what I consider the starting point dataset to begin the modeling with HBV.IANIGLA. This data is for modeling the streamflow of a synthetic basin with a perfect fit. For running the model you will have to connect the different package's modules (or functions) in order to get what I consider the most simple hydrological model.

Usage

lumped_hbv

Format

A data frame containing:

Date

date series.

T(ºC)

air temperature series.

P(mm/d)

total ammount of precipitation per day.

PET(mm/d)

potential evapotranspiration series.

qout(mm/d)

specific basin discharge. This are the values that you have to reproduce.

---

Atmospheric pressure

Description

Calculate the atmospheric pressure using the altitude.

Arguments

z	a double representing the altitude $[masl]$.

Value

A double with the atmospheric pressure $[kPa]$.

---

Potential evapotranspiration models

Description

Calculate your potential evapotranspiration series. This module was design to provide a simple and straight forward way to calculate one of the inputs for the soil routine (to show how does it works), but for real world application I strongly recommend the use of the specialized Evapotranspiration package.

Usage

PET(
  model,
  hemis,
  inputData,
  elev,
  param
  )

Arguments

model	numeric value with model option: 1: Calder's model.
hemis	numeric value indicating the hemisphere: 1: southern hemisphere. 2: northern hemisphere.
inputData	numeric matrix with the following columns: Calder's model column_1: julian dates, e.g: as.matrix( c(1:365) ).
elev	numeric vector with the following values: Calder's model 1: zref: the reference height where potential evapotranspiration or input data to calculate PET is known. 2: ztopo: target PET's topographic height.
param	numeric vector with the following values: Calder's model 1: PET: climatological daily mean potential evapotranspiration [mm]. 2: gradPET: evapotranspiration decrease gradient [mm/100 m].

Value

Numeric vector with the potential evapotranspiration series.

References

Calder, I.R., Harding, R.J., Rosier, P.T.W., 1983. An objective assessment of soil-moisture deficit models. J. Hydrol. 60, 329–355. https://doi.org/10.1016/0022-1694(83)90030-6

Examples

# The following is a toy example. I strongly recommend to see
# the package vignettes in order to improve your skills on HBV.IANIGLA

## Run the model for a year in the southern hemisphere
potEvap <- PET(model = 1,
               hemis = 1,
               inputData = as.matrix(1:365),
               elev = c(1000, 1500),
               param = c(4, 0.5))

---

Altitude gradient based precipitation models

Description

Extrapolate precipitation gauge measurements to another heights. In this package version you can use the classical linear gradient model or a modified version which sets a threshold altitude for precipitation increment (avoiding unreliable estimations).

Usage

Precip_model(
       model,
       inputData,
       zmeteo,
       ztopo,
       param
)

Arguments

model	numeric value with model option: 1: linear precipitation gradient (LP). 2: linear precipitation gradient with an upper threshold (LPM).
inputData	numeric vector with precipitation gauge series $[mm/\Delta t]$.
zmeteo	numeric value indicating the altitude of the precipitation gauge $[masl]$.
ztopo	numeric value with the target height $[masl]$.
param	numeric vector with the following parameters: LP 1: precipitation gradient (gradP) [%/100m]. LPM 1: precipitation gradient (gradP) [%/100m]. 2: threshold height. Precipitation does not increase when the altitude (ztopo) is higher than this parameter $[masl]$.

Value

Numeric vector with the extrapolated precipitation series.

References

For some interesting work on precipitation gradients at catchment and synoptic scale see:

Immerzeel, W.W., Petersen, L., Ragettli, S., Pellicciotti, F., 2014. The importance of observed gradients of air temperature and precipitation for modeling runoff from a glacierized watershed in the Nepalese Himalayas. Water Resour. Res. 50, 2212–2226. https://doi.org/10.1002/2013WR014506

Viale, M., Nuñez, M.N., 2010. Climatology of Winter Orographic Precipitation over the Subtropical Central Andes and Associated Synoptic and Regional Characteristics. J. Hydrometeorol. 12, 481–507. https://doi.org/10.1175/2010JHM1284.1

Examples

# The following is a toy example. I strongly recommend to see
# the package vignettes in order to improve your skills on HBV.IANIGLA

## LP case
set.seed(369)

precLP <- Precip_model(model = 1, inputData = runif(n = 365, max = 30, min = 0),
                        zmeteo = 3000, ztopo = 4700, param = c(5))

## LPM case
set.seed(369)

precLPM <- Precip_model(model = 2, inputData = runif(n = 365, max = 30, min = 0),
                        zmeteo = 3000, ztopo = 4700, param = c(5, 4500))

---

Precipitation phase - Ding et al. (2014)

Description

Estimate precipitation phase partioning based on Tair and RH

Arguments

tair	recorded air temperature $[ºC]$.
rh	relative humidity $[\%]$.
z	double with meteorological station altitude $[masl]$.

Value

A numeric vector with: * the snowfall fraction $[-]$ * the rainfall fraction $[-]$

Note

The model was developed using daily data.

---

Precipitation phase - Harder and Pomeroy (2013)

Description

Estimate precipitation phase partioning based on Tair and RH

Arguments

tair	recorded air temperature $[ºC]$.
rh	relative humidity $[\%]$.
error_thres	double with absolute error. This value is used as a convergence criteria in the Newton-Raphson method.
period	integer value (1, 2 or 3), where: * 1 => 15 min record period * 2 => 1 hour record period * 3 => 1 day record period

Value

A numeric vector with: * the snowfall fraction $[-]$ * the rainfall fraction $[-]$ * hydrometeor temperature $[ºC]$ * the required number of iterations $[-]$

---

Routing bucket type models

Description

Implement one of the five different bucket formulations for runoff routing. The output of this function is the input series of the transfer function (UH).

Usage

Routing_HBV(
       model,
       lake,
       inputData,
       initCond,
       param
       )

Arguments

model	numeric integer indicating which reservoir formulation to use: 1: Three series of reservoirs. Lake option is allowed. 2: Two series of reservoirs. Lake option is allowed. 3: Two reservoirs and three outlets. Lake option is allowed. 4: One reservoir and two outlets. Lake is NOT allowed. 5: One reservoir and three outlets. Lake is NOT allowed.
lake	logical. A TRUE value will enable the lake option (only available on models 1, 2 and 3). When modeling a lake, HBV.IANIGLA considers that this water body exist on the bottom bucket, so you will also have to provide a lake evaporation and precipitation series in the inputData matrix.
inputData	numeric matrix with three columns (two of them depends on lake option). column_1: effective runoff series $[mm/\Delta T]$. This is the output of the Soil_HBV module. column_2: only if lake = TRUE. Precipitation series falling in the lake. When using it remember that the precipitation should be rescaled according to the relative area of the lake in the basin. column_3: only if lake = TRUE. Lake's evaporation series. When using it remember that the precipitation should be rescaled according to the relative area of the lake in the basin.
initCond	numeric vector with the following initial state variables. SLZ0: initial water content of the lower reservoir $[mm]$. This state variable is compulsory for all model options. SUZ0: initial water content of the intermediate reservoir $[mm]$. This option does not make sense for models 4 and 5. STZ0: initial water content of the upper reservoir $[mm]$. This option only make sense for model 1.
param	numeric vector. The length depends on the model's choice: Model 1 K0: top bucket (STZ) storage constant $[1/\Delta t]$. K1: intermediate bucket (SUZ) storage constant $[1/\Delta t]$. K2: lower bucket (SLZ) storage constant $[1/\Delta t]$. UZL: maximum flux rate between STZ and SUZ $[mm/\Delta t]$. PERC: maximum flux rate between SUZ and SLZ $[mm/\Delta t]$. Model 2 K1: intermediate bucket (SUZ) storage constant $[1/\Delta t]$. K2: lower bucket (SLZ) storage constant $[1/\Delta t]$. PERC: maximum flux rate between SUZ and SLZ $[mm/\Delta t]$. Model 3 K0: top output (Q0) storage constant $[1/\Delta t]$. K1: intermediate bucket (SUZ) storage constant $[1/\Delta t]$. K2: lower bucket (SLZ) storage constant $[1/\Delta t]$. UZL: minimum water content of SUZ for supplying fast runoff (Q0) to the total reservoir discharge (Qg) $[mm]$. PERC: maximum flux rate between SUZ and SLZ $[mm/\Delta t]$. Model 4 K1: intermediate output (Q1) storage constant $[1/\Delta t]$. K2: lower bucket (SLZ) storage constant $[1/\Delta t]$. PERC: minimum water content of SLZ for supplying intermediate runoff (Q1) to the total reservoir discharge (Qg) $[mm]$. Model 5 K0: top output (Q0) storage constant $[1/\Delta t]$. K1: intermediate output (Q1) storage constant $[1/\Delta t]$. K2: lower bucket (SLZ) storage constant $[1/\Delta t]$. UZL: minimum water content of SLZ for supplying fast runoff (Q0) to the total reservoir discharge (Qg) $[mm]$. PERC: minimum water content of SLZ for supplying intermediate runoff (Q1) to the total reservoir discharge (Qg) $[mm]$.

Value

Numeric matrix with the following columns:

Model 1

• Qg: total buckets output discharge $[mm/\Delta t]$.

• Q0: top bucket discharge $[mm/\Delta t]$.

• Q1: intermediate bucket discharge $[mm/\Delta t]$.

• Q2: lower bucket discharge $[mm/\Delta t]$.

• STZ: top reservoir storage $[mm]$.

• SUZ: intermediate reservoir storage $[mm]$.

• SLZ: lower reservoir storage $[mm]$.

Model 2

• Qg: total buckets output discharge $[mm/\Delta t]$.

• Q1: intermediate bucket discharge $[mm/\Delta t]$.

• Q2: lower bucket discharge $[mm/\Delta t]$.

• SUZ: intermediate reservoir storage $[mm]$.

• SLZ: lower reservoir storage $[mm]$.

Model 3

• Qg: total buckets output discharge $[mm/\Delta t]$.

• Q0: intermediate bucket fast discharge $[mm/\Delta t]$.

• Q1: intermediate bucket discharge $[mm/\Delta t]$.

• Q2: lower bucket discharge $[mm/\Delta t]$.

• SUZ: intermediate reservoir storage $[mm]$.

• SLZ: lower reservoir storage $[mm]$.

Model 4

• Qg: total buckets output discharge $[mm/\Delta t]$.

• Q1: lower bucket intermediate discharge $[mm/\Delta t]$.

• Q2: lower bucket discharge $[mm/\Delta t]$.

• SLZ: lower reservoir storage $[mm]$.

Model 5

• Qg: total buckets output discharge $[mm/\Delta t]$.

• Q0: lower bucket fast discharge $[mm/\Delta t]$.

• Q1: lower bucket intermediate discharge $[mm/\Delta t]$.

• Q2: lower bucket discharge $[mm/\Delta t]$.

• SLZ: lower reservoir storage $[mm]$.

References

Bergström, S., Lindström, G., 2015. Interpretation of runoff processes in hydrological modelling—experience from the HBV approach. Hydrol. Process. 29, 3535–3545. https://doi.org/10.1002/hyp.10510

Beven, K.J., 2012. Rainfall - Runoff Modelling, 2 edition. ed. Wiley, Chichester.

Seibert, J., Vis, M.J.P., 2012. Teaching hydrological modeling with a user-friendly catchment-runoff-model software package. Hydrol Earth Syst Sci 16, 3315–3325. https://doi.org/10.5194/hess-16-3315-2012

Examples

# The following is a toy example. I strongly recommend to see
# the package vignettes in order to improve your skills on HBV.IANIGLA

## Case example with the first model
inputMatrix <- cbind(
                     runif(n = 200, max = 100, min = 0),
                     runif(n = 200, max = 50, min = 5),
                     runif(n = 100, max = 3, min = 1)
                     )

routeMod1   <- Routing_HBV(model = 1, lake = TRUE, inputData = inputMatrix,
                     initCond = c(10, 15, 20), param = c(0.1, 0.05, 0.001, 1, 0.8))

---

Semi-distributed HBV model data

Description

Here you will find the lumped model's next step. A semi-distributed model seems more similar to what we try to simulate in real world hydrology. This dataset allows you to experiment with a synthetic HBV.IANIGLA semi-distributed exercise.

Usage

semi_distributed_hbv

Format

A list with five elements

basin

data frame containing elevation band names and the hypsometric values for modeling the catchment.

tair

numeric matrix with the air temperature series (columns) for the 15 elevation bands.

prec

numeric matrix with the precipitation series (columns) for the 15 elevation bands.

pet

numeric matrix with the potential evapotranspiration series (columns) for the 15 elevation bands.

qout

numeric vector with the synthetic catchment discharge.

---

Snow and ice-melt models

Description

Allows you to simulate snow accumulation and melting processes using a temperature index approach. The function also incorporates options for clean and debris covered glacier surface mass balance simulations.

Usage

SnowGlacier_HBV(
       model,
       inputData,
       initCond,
       param
)

Arguments

model	numeric indicating which model you will use: 1: temperature index model. 2: temperature index model with a variable snow cover area as input data (as in the Snowmelt Runoff Model - SRM). 3: temperature index model with a variable glacier area as input data.
inputData	numeric matrix being columns the input variables. As in the whole package functions, NA_real_ values are forbidden. When speaking about model options we refer to the model argument. Model 1: column_1: air temperature series $[°C/\Delta t]$. column_2: precipitation series $[mm/\Delta t]$. Model 2: column_1: air temperature $[°C/\Delta t]$. column_2: precipitation $[mm/\Delta t]$. column_3: snow cover area. Values between [0 ; 1] $[-]$. Model 3: column_1: air temperature $[°C/\Delta t]$. column_2: precipitation $[mm/\Delta t]$. column_3: glacier cover area. This area values are relative to the total surface area of the basin $[-]$.
initCond	numeric vector with the following values. SWE0: initial snow water equivalent $[mm]$. numeric integer indicating the surface type. 1: clean ice; 2: soil; 3: debris-covered ice. area of the glacier(s) (in the elevation band) relative to the basin; e.g.: 0.1 $[-]$. This option is required in Model 1 and Model 2 when surface is a glacier.
param	numeric vector with the following values: SFCF: snowfall correction factor $[-]$. Tr: solid and liquid precipitation threshold temperature $[ºC]$. Tt: melt temperature $[ºC]$. fm: snowmelt factor $[mm/°C.\Delta t]$. fi: icemelt factor $[mm/°C.\Delta t]$. fic: debris-covered ice-melt factor $[mm/°C.\Delta t]$.

Value

Numeric matrix with the following columns:

Model 1

** if surface is soil,

1. Prain: precip. as rainfall.

2. Psnow: precip. as snowfall.

3. SWE: snow water equivalent.

4. Msnow: melted snow.

5. Total: Prain + Msnow.

** if surface is ice,

1. Prain: precip. as rainfall.

2. Psnow: precip. as snowfall.

3. SWE: snow water equivalent.

4. Msnow: melted snow.

5. Mice: melted ice.

6. Mtot: Msnow + Mice.

7. Cum: Psnow - Mtot.

8. Total: Prain + Mtot.

9. TotScal: Total * initCond[3].

Model 2

** if surface is soil,

1. Prain: precip. as rainfall.

2. Psnow: precip. as snowfall.

3. SWE: snow water equivalent.

4. Msnow: melted snow.

5. Total: Prain + Msnow.

6. TotScal: Msnow * SCA + Prain.

** if surface is ice -> as in Model 1

Model 3

** if surface is soil -> as in Model 1

** if surface is ice,

1. Prain: precip. as rainfall.

2. Psnow: precip. as snowfall.

3. SWE: snow water equivalent.

4. Msnow: melted snow.

5. Mice: melted ice.

6. Mtot: Msnow + Mice.

7. Cum: Psnow - Mtot.

8. Total: Prain + Mtot.

9. TotScal: Total * inputData[i, 3].

References

Bergström, S., Lindström, G., 2015. Interpretation of runoff processes in hydrological modelling—experience from the HBV approach. Hydrol. Process. 29, 3535–3545. https://doi.org/10.1002/hyp.10510

DeWalle, D. R., & Rango, A. (2008). Principles of Snow Hydrology.

Parajka, J., Merz, R., Blöschl, G., 2007. Uncertainty and multiple objective calibration in regional water balance modelling: case study in 320 Austrian catchments. Hydrol. Process. 21, 435–446. https://doi.org/10.1002/hyp.6253

Seibert, J., Vis, M.J.P., 2012. Teaching hydrological modeling with a user-friendly catchment-runoff-model software package. Hydrol Earth Syst Sci 16, 3315–3325. https://doi.org/10.5194/hess-16-3315-2012

Examples

# The following is a toy example. I strongly recommend to see
# the package vignettes in order to improve your skills on HBV.IANIGLA

## Debris-covered ice
ObsTemp   <- sin(x = seq(0, 10*pi, 0.1))
ObsPrecip <- runif(n = 315, max = 50, min = 0)
ObsGCA    <- seq(1, 0.8, -0.2/314)

## Fine debris covered layer assumed. Note that the ice-melt factor is cumpulsory but harmless.
DebrisCovGlac <- SnowGlacier_HBV(model = 3,
                                 inputData = cbind(ObsTemp, ObsPrecip, ObsGCA),
                                 initCond = c(10, 3, 1),
                                 param = c(1, 1, 0, 3, 1, 6))

---

Empirical soil moisture routine

Description

This module allows you to account for actual evapotranspiration, abstractions, antecedent conditions and effective runoff. The formulation enables non linear relationships between soil box water input (rainfall plus snowmelt) and the effective runoff. This effective value is the input series to the routine function (Routing_HBV).

Usage

Soil_HBV(
       model,
       inputData,
       initCond,
       param
       )

Arguments

model	numeric integer suggesting one of the following options: 1: Classical HBV soil moisture routine. 2: HBV soil moisture routine with varying area. This option should be used with SnowGlacier_HBV's model 3.
inputData	numeric matrix with the following series Model 1 column_1: Total = Prain + Msnow $[mm/\Delta t]$. This series comes from the output of the SnowGlacier_HBV module. column_2: potential evapotranspiration $[mm/\Delta t]$. Since the package has a simple model (PET) to obtain this series I strongly recommend using the Evapotranspiration package. Model 2 column_1: as in model 1. column_2: as in model 1. column_3 : relative soil area (ratio of soil surface over basin area). When the glacier area changes the soil does the same, so coherence between this two series should be seek.This value is used to scale the effective runoff accordingly (Rech column in the matrix output).
initCond	numeric vector with the following values: initial soil water content $[mm]$. This is a model state variable and is internally used as first soil moisture value. relative area $[-]$. Only needed when using model 1. This is the soil surface proportion relative to the catchment as a whole, so the values should never supersede one (1). This value is used to scale the effective runoff accordingly (Rech column in the matrix output).
param	numeric vector with the following values: FC: fictitious soil field capacity $[mm]$. LP: parameter to get actual ET $[-]$. $\beta$: exponential value that allows for non-linear relations between soil box water input (rainfall plus snowmelt) and the effective runoff $[-]$.

Value

Numeric matrix with the following columns:

1. Rech: recharge series $[mm/\Delta t]$. This is the input to the Routing_HBV module.

2. Eact: actual evapotranspiration series $[mm/\Delta t]$.

3. SM: soil moisture series $[mm/\Delta t]$.

References

Bergström, S., Lindström, G., 2015. Interpretation of runoff processes in hydrological modelling—experience from the HBV approach. Hydrol. Process. 29, 3535–3545. https://doi.org/10.1002/hyp.10510

Examples

# The following is a toy example. I strongly recommend to see
# the package vignettes in order to improve your skills on HBV.IANIGLA

# HBV soil routine with variable area
## Calder's model
potEvap <- PET(model = 1, hemis = 1, inputData = as.matrix(1:315), elev = c(1000, 1500),
              param = c(4, 0.5))

## Debris-covered ice
 ObsTemp   <- sin(x = seq(0, 10*pi, 0.1))
 ObsPrecip <- runif(n = 315, max = 50, min = 0)
 ObsGCA    <- seq(1, 0.8, -0.2/314)

## Fine debris covered layer assumed. Note that the ice-melt factor is cumpulsory but harmless.
DebrisCovGlac <- SnowGlacier_HBV(model = 3, inputData = cbind(ObsTemp, ObsPrecip, ObsGCA),
                                 initCond = c(10, 3, 1), param = c(1, 1, 0, 3, 1, 6))

## Soil routine
ObsSoCA     <- 1 - ObsGCA
inputMatrix <- cbind(DebrisCovGlac[ , 9], potEvap, ObsSoCA)

soil <- Soil_HBV(model = 2, inputData = inputMatrix, initCond = c(50), param = c(200, 0.5, 2))

---

Empirical soil moisture routine

Description

Accounts for actual evapotranspiration, abstractions, antecedent conditions and effective runoff. The formulation enables non linear relationships between soil box water input (rainfall plus snowmelt) and the effective runoff. This effective value is the input series to the routine function (do_route).

Usage

soil_hbv_pro(
       inputData,
       initCond,
       param
       )

Arguments

inputData	numeric matrix with the following series: column_1: Total = Prain + Msnow $[mm/\Delta t]$. This series comes from the output of the do_snow module. column_2: potential evapotranspiration $[mm/\Delta t]$. column_3: snow water equivalent $[mm/\Delta t]$. If snow exists above the ground, actual evap. will be zero.
initCond	numeric vector with the following values: initial soil water content $[mm]$. This is a model state variable and is internally used as first soil moisture value. relative area $[-]$. Default value is one.
param	numeric vector with the following values: FC: fictitious soil field capacity $[mm]$. LP: parameter to get actual ET $[-]$. $\beta$: exponential value that allows for non-linear relations between soil box water input (rainfall plus snowmelt) and the effective runoff $[-]$.

Value

Numeric matrix with the following columns:

1. Rech: recharge series $[mm/\Delta t]$.

2. Eact: actual evapotranspiration series $[mm/\Delta t]$.

3. SM: soil moisture series $[mm/\Delta t]$.

---

Altitude gradient base air temperature models

Description

Extrapolate air temperature records to another heights. In this package version you can use the classical linear gradient model or a modified version which sets an upper altitudinal threshold air temperature decrement (avoiding unreliable estimations).

Usage

Temp_model(
       model,
       inputData,
       zmeteo,
       ztopo,
       param
)

Arguments

model	numeric value with model option: 1: linear air temperature gradient (LT). 2: linear air temperature gradient with an upper threshold (LTM).
inputData	numeric vector with air temperature record series [ºC/$\Delta t$].
zmeteo	numeric value indicating the altitude where the air temperature is recorded $[masl]$.
ztopo	numeric value with the target height $[masl]$.
param	numeric vector with the following parameters: LT 1: air temperature linear gradient (grad_t) [ºC/km]. LPM 1: air temperature linear gradient (grad_t) [ºC/km]. 2: threshold height. Air temperature does not decrease when the altitude (ztopo) is higher than this value $[masl]$.

Value

Numeric vector with the extrapolated air temperature series.

References

Immerzeel, W.W., Petersen, L., Ragettli, S., Pellicciotti, F., 2014. The importance of observed gradients of air temperature and precipitation for modeling runoff from a glacierized watershed in the Nepalese Himalayas. Water Resour. Res. 50, 2212–2226. https://doi.org/10.1002/2013WR014506

Examples

# The following is a toy example. I strongly recommend to see
# the package vignettes in order to improve your skills on HBV.IANIGLA

## simple linear model
airTemp <- Temp_model(
                      model = 1,
                      inputData = runif(200, max = 25, min = -10),
                      zmeteo = 2000, ztopo = 3500, param = c(-6.5)
                      )

---

Tupungato River basin data

Description

A dataset containing a minimal information to simulate the streamflow discharge of the Tupungato catchment. The basin is located in the north of the Mendoza province (Argentina - 32.90º S; 69.76º W) and has an area of about 1769 $km^2$. This catchment is the main tributary of the Mendoza River basin (~50 % of the annual discharge), a stream that supplies with water to most of the province population (~64 %).

Usage

tupungato_data

Format

A list with four elements

hydro_meteo

data frame with the air temperature, precipitation and streamflow (mean, lower and upper bounds) series.

snow_cover

data frame containing the snow cover (from MODIS) series for each elevation band.

topography

data frame with: elevation zone number, minimum, maximum and mean altitude values for the elevation range and the relative area of each polygon.

station_height

numeric vector with the station (Toscas) height (in masl).

---

Transfer function

Description

Use a triangular transfer function to adjust the timing of the simulated streamflow discharge. This module represents the runoff routing in the streams.

Usage

UH(
  model,
  Qg,
  param
  )

Arguments

model	numeric integer with the transfer function model. The current HBV.IANIGLA model only allows for a single option. 1: triangular function with a static base.
Qg	numeric vector with the water that gets into the stream. If you are not modeling glaciers is the output of the Routing_HBV module, otherwise, is the sum of the Routing_HBV output plus the glacier discharge coming from the Glacier_Disch module.
param	numeric vector with the following values, Model 1 Bmax: base of the transfer function triangle $[timestep]$.

Value

Numeric vector with the simulated streamflow discharge.

References

Bergström, S., Lindström, G., 2015. Interpretation of runoff processes in hydrological modelling—experience from the HBV approach. Hydrol. Process. 29, 3535–3545. https://doi.org/10.1002/hyp.10510

Parajka, J., Merz, R., & Blöschl, G. (2007). Uncertainty and multiple objective calibration in regional water balance modelling: Case study in 320 Austrian catchments. Hydrological Processes, 21(4), 435-446. https://doi.org/10.1002/hyp.6253

Examples

# The following is a toy example. I strongly recommend to see
# the package vignettes in order to improve your skills on HBV.IANIGLA

## Routing example
inputMatrix <- cbind(runif(n = 200, max = 100, min = 0), runif(n = 200, max = 50, min = 5),
                 runif(n = 100, max = 3, min = 1))

routeMod1   <- Routing_HBV(model = 1, lake = TRUE, inputData = inputMatrix,
                         initCond = c(10, 15, 20), param = c(0.1, 0.05, 0.001, 1, 0.8))

## UH
dischOut <- UH(model = 1, Qg = routeMod1[ , 1], param = 2.2)

---

Precipitation phase - Ding et al. (2014).

Description

Estimate precipitation phase partioning based on Tair and RH. Vectorised version.

Arguments

tair	rnumeric vecto with recorded air temperature $[ºC]$.
rh	numeric vector with relative humidity $[\%]$.
z	double with meteorological station altitude $[masl]$.

Value

A numeric vector with: * the snowfall fraction $[-]$ * the rainfall fraction $[-]$

Note

The model was developed using daily data.

---

Precipitation phase - Harder and Pomeroy (2013)

Description

Estimate precipitation phase partioning based on Tair and RH (vectorised version).

Arguments

tair	numeric vector with recorded air temperature $[ºC]$.
rh	numeric vector with relative humidity $[\%]$.
delta_x	double with increment to derivate using the limit's concept.
error_thres	double with absolute error. This value is used as a convergence criteria in the Newton-Raphson (secant) method.
period	character with: * "15 min" => 1 * "1 hour" => 2 * "1 day" => 3

Value

A numeric matrix with two columns: * 1. the snowfall fraction $[-]$ * 2. the rainfall fraction $[-]$

---